This paper is based on [CPSSZ00] which is to appear in Experimental Mathematics. The name wavelet was made up by French researchers [MAFG82, Mor83, GM84] for a particular class of functions. The existence of wavelet-like functions has been known since the beginning of the century (a notable example is what is known as the Haar wavelet today [Haa10]). However, only recently the unifying concepts...

In this work, we present a computational method for solving Poisson equations and biharmonic equations which are based on the use of Haar wavelets. The first transform the spectral coefficients into the nodal variable values. The second use Kronecker products to construct the approximations for derivatives over a tensor product grid of the horizontal and vertical blocks. Finally, solve the obta...

Este artigo desenvolve uma metodologia numérica, utilizando conjuntamente as plataformas computacionais ANSYS® e Matlab®, para localizar quantificar danos estruturais em treliças vigas. Esses sistemas são modelados numericamente via Método dos Elementos Finitos no ANSYS®, posteriormente, o sinal (deflexão) sofrida pela estrutura é transformado Transformada Contínua de Wavelet (TW) Matlab®. A mo...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

In this work, we present a computational method for solving double and triple integrals with variable limits of integrations which is based on Haar wavelets. This approach is the generalization and improvement of the methods [3]. The advantage of this new methods is its more efficient and simple applicability than the previous methods. Error analysis for the case of two dimension are considered...

The generators of binary multiplicative cascade models with a non-overlapping branching structure are given by the Haar wavelets. We construct specific generalizations of these models for which any given wavelet represents the generators of the local cascade branchings. Such "wavelet cascades", for which we calculate spatial correlation functions, have spatially overlapping branches and are the...

In this paper, we present a method for calculated the numerical approximation of nonlinear Fredholm Volterra Hammerstein integral equation, which uses the properties of rationalized Haar wavelets. The main tool for error analysis is the Banach fixed point theorem. An upper bound for the error was obtained and the order of convergence is analyzed. An algorithm is presented to compute and illustr...